The present invention pertains generally to plasma apparatus and processes for use in material separation applications. More particularly, the present invention pertains to apparatus which are capable of separating ions in a plasma according to their respective mass to charge ratio. The present invention is particularly, but not exclusively, useful for separating ions in a plasma according to their respective mass to charge ratios using ponderomotive forces.
For applications wherein the purpose is to separate one constituent element from a multi-constituent material, such as a chemical mixture of elements or isotopes, there are several possible ways to proceed. In some instances, mechanical separation may be possible. In others, chemical separation may be more appropriate. When mechanical or chemical processes are not feasible, however, it may happen that separation procedures and processes involving plasma physics may be necessary. To do this, a multi-species plasma needs to be made from the chemical mixture and the resultant ions separated according to their respective mass to charge ratios.
Ion separation can be accomplished in several ways known in the pertinent art. For example, plasma centrifuges and their methods of operation are well known. On the other hand, and not yet so well known, plasma filters and their methods of operation are also useful for this purpose. For example, the invention as disclosed by Ohkawa in U.S. Pat. No. 6,096,220 which issued on Aug. 1, 2000, for an invention entitled xe2x80x9cPlasma Mass Filterxe2x80x9d and which is assigned to the same assignee as the present invention, is useful for separating ions of different mass to charge ratios. Quite different from the above described techniques, the present invention contemplates the use of ponderomotive forces to separate ions in a multi-species plasma according to their mass to charge ratios.
It is well known that photons carry momentum. When a wave of photons (i.e. an electromagnetic wave) is evanescent in a medium, reflection of the wave occurs. When a photon is reflected from a media, momentum is transferred from the photon to the medium. Importantly, this momentum transfer exerts a force (a ponderomotive force) on the medium. In the case where the medium is a plasma, a force is exerted on the individual particles (ions and electrons) in the plasma. Along these lines, co-pending application Ser. No. 10/086,575 entitled xe2x80x9cPonderomotive Force End Plug For A Plasma Mass Filterxe2x80x9d by Tihiro Ohkawa filed concurrently herewith now allowed and which is assigned to the same assignee as the present invention, discloses the use of ponderomotive forces to create an end plug for a plasma chamber. The contents of the co-pending allowed application entitled xe2x80x9cPonderomotive Force End Plug For A Plasma Mass Filterxe2x80x9d are hereby incorporated by reference.
In a uniform, stationary magnetic field, the ions and electrons in a plasma will rotate in oppositely directed orbits. If a circularly polarized electromagnetic wave is propagating in the direction of the magnetic field, two distinct polarization modes are possible for the electromagnetic wave; a right-hand polarized mode and a left-hand polarized mode. In the right-hand mode, the electric field of the electromagnetic wave rotates in the same direction as the gyration of the electrons in the stationary magnetic field. In contrast, in the left-hand mode, the electric field of the electromagnetic wave rotates in the opposite direction as the gyration of the electrons in the stationary magnetic field.
Importantly for the present application, a left-hand polarized mode electromagnetic wave having specifically tailored characteristics can impart ponderomotive forces on ions, the direction of which will vary depending on the mass to charge ratio of the ion. Stated differently, for a plasma that contains multiple species of ions, the low-mass ions with the cyclotron frequencies higher than the frequency of the left-hand polarized mode electromagnetic wave are forced to move in one direction while the electrons and the high-mass ions are forced to move in the opposite direction.
To make the plasma dielectric negative, the sum of the ponderomotive forces on all charged particles must be confining (i.e. directed away from the source of the electromagnetic wave). Since each species receives a different force, an electrostatic field build up occurs due to the ambipolar effect. The steady state can be calculated by starting with the contribution xcex5s of a single charged particle to the plasma dielectric in the left-hand polarized mode, which is given by:
xcex5s={e2/mxcfx89[xe2x88x92xcexa9]}xe2x80x83xe2x80x83[1]
where m is the mass, xcfx89 is the wave frequency and xe2x89xa0 is the cyclotron frequency of the charged particle including the sign. For convenience, the following convention is used; xcfx89 greater than 0, xcexa9i greater than 0 and xcexa9e less than 0.
The ponderomotive force, f, on the particle is given by
f={e2/mxcfx89[xe2x88x92xcfx89+xcexa9]}[xc2xd][∇E2]xe2x80x83xe2x80x83[2]
where E is the electric field of the wave. The sign (i.e. direction) of the ponderomotive force is directly related to the sign of the dielectric contribution. The ponderomotive potential U can be defined by
U={e2/mxcfx89[xe2x88x92xcfx89+xcexa9]}[E2/2].xe2x80x83xe2x80x83[3]
The force balance equations for the electrons and the ions are given by
xe2x88x92∇pexe2x88x92ne∇Ue+e ne∇"PHgr"=0
and
xe2x88x92∇pixe2x88x92ni∇Uixe2x88x92e ni∇"PHgr"=0xe2x80x83xe2x80x83[4]
where p is the pressure and "PHgr" is the electrostatic potential.
Consider now a plasma with two ion species [subscript 1 and 2]. By assuming equal and uniform temperature T, the following equations are obtained:
∇{xe2x88x92T In nexe2x88x92Ue+e"PHgr"}=0
∇{xe2x88x92T In n1,2xe2x88x92U1,2xe2x88x92e"PHgr"}=0xe2x80x83xe2x80x83[5]
n1+n2=ne.
By eliminating "PHgr", the following equations are obtained:
n12={n1,02neexp[[U2xe2x88x922U1xe2x88x92Ue]/T]{}n2,0+n1,0exp[U2xe2x88x92U1]/T}xe2x88x921
n22={n2,02ne exp[[U2xe2x88x92Ue]/T]{}n2,0+n1,0exp[U2xe2x88x92U1]/T}xe2x88x921xe2x80x83xe2x80x83[6]
where the subscript 0 denotes the quantities away from the source of the electromagnetic wave.
The ratio of the densities is given by
n2/n1=[n20/n10]exp[xe2x88x92U2+U1]/Txe2x80x83xe2x80x83[7]
and
[xe2x88x92U2+U1]/T={e2E2/Txcfx89[xcexa92xe2x88x92xcexa91]}[M1xe2x88x921+M2xe2x88x921].xe2x80x83xe2x80x83[8]
Thus, the concentration of the low-mass ions, M1, increases away from the source of the electromagnetic wave.
Since the low-mass ions are not confined, the above equilibrium is fictitious. The equation for the low-mass ions should contain the velocity term
xe2x88x92∇p2xe2x88x92∇{M2v22/2+U2+e"PHgr"}=0.xe2x80x83xe2x80x83[9]
The uniform temperature assumption may not be correct but it can be used to see a trend, namely
∇[T In n2+M2v22/2+U2+e"PHgr"]=0.xe2x80x83xe2x80x83[10]
The above equation is the same as eq. [5] if U2 is replaced by U2+M2 v22/2. The solution given by eq. [6] holds with the substitution. The solution is made self consistent with
n2 v2=xcex932=const.
If the magnitude of the ponderomotive potentials for the electrons and the ions are comparable, eq. [10] shows that the unconfined ions stream out at the sound velocity.
Useful results can be obtained by using the concentration ratio given by eq [7]. The optimum frequency is given by
xcfx89=[xcexa91+xcexa92]/2xe2x80x83xe2x80x83[11]
and
[U1xe2x88x92U2]/T={2E2M1M2/B02[M1xe2x88x92M2]T}.xe2x80x83xe2x80x83[12]
The required field is small for a mass difference that is small, such as isotopes. However, the density limit resulting from the ion-ion collisions is lower.
The dispersion equation is given by
k2=[xcfx892/c2]{1+xcexa3xcfx89p2/xcfx89[xe2x88x92xcfx89+xcexa9]}xe2x88x92xcex2xe2x80x83xe2x80x83[13]
where k is the axial wave number, X is the radial wave number, xcfx89p2=e2 nj/xcex50 Mj, and xcexa3 is the sum over all species. It is important to keep the wave evanescent, and the concentration of the low-mass ions is limited by this condition. For the choice of the frequency given by eq [11], the limit is n2 less than ne/2 in the limit of xcex=0.
For steady state bulk separation where the goal is to produce low-mass ions, the first end of the separator is plugged and contains the electromagnetic wave source. The second end is open. The first end receives one half of the low-mass ions and no high-mass ions. The second end receives all of the high-mass ions and one half of the low-mass ions. If the desired product is the high-mass ions, the second end is opened periodically. While the second end is plugged, the first end receives almost all low-mass ions. The second end can be opened to allow all of the remaining ions to exit the second end. The cycle is repeated until the desired purity of high-mass ions is obtained.
The separation throughput is also limited by collisional effects. Both electron and ion collisions dissipate the power of the electromagnetic wave. At some point the dissipation becomes so great that the ponderomotive force is ineffective. Also, the ion collisions blur the difference between the ion cyclotron frequencies among the different ion species. This is especially true for the isotope separation where the difference between the isotopes is small.
Consider now the motion of a charged particle with charge, q, and mass, M, under the electric field given by
Ex+iEy=Eexp[xe2x88x92ixcfx89t+kz].xe2x80x83xe2x80x83[14a]
The magnetic field is given by
Bx+iBy=[xcfx89/k]Eexp[xe2x88x92ixcfx89t+kz].xe2x80x83xe2x80x83[14b]
The equation of motion becomes
xe2x80x83Mdvx/dt=qEx+qvyB0
Mdvy/dt=qEyxe2x88x92qvxB0
Mdvz/dt=Fz=q[vxByxe2x88x92vyBx].xe2x80x83xe2x80x83[14c]
from which the following relationships are obtained:
vx+ivy=xe2x88x92i[q/M][xe2x88x92xcfx89+xcexa9]xe2x88x921Eexp[xe2x88x92xcfx89t+kz].xe2x80x83xe2x80x83[14d]
When the collision frequency is included in eq. [14d], the result is
vx+ivy=e[Ex+iEy]/{m[ixcfx89xe2x88x92ixcexa9+xcexd]}.xe2x80x83xe2x80x83[14e]
The power dissipation P for each species is given by
P=enRe[vxxe2x88x92ivy][Ex+Ey]xe2x80x83xe2x80x83[15]
=[e2n/m]xcexdE2/{[xcfx89xe2x88x92xcexa9]2+xcexd2}.xe2x80x83xe2x80x83[16]
By relating the power to the ponderomotive potential, the result is
P=2xcexdxcfx89[xcfx89xe2x88x92xcexa9]{[xcfx89xe2x88x92xcexa9]2+xcexd2}xe2x88x921n U.xe2x80x83xe2x80x83[17]
For electrons, xcfx89 less than  less than |xcexa9| and xcexde less than  less than xcexa9e,
Pe≈2 xcexde[xcfx89/xcexa9e]ne Ue.xe2x80x83xe2x80x83[18]
For the ions, assuming xcexdi less than  less than |xcfx89xe2x88x92xcexa9i| the result is
Pi≈2 xcexdi[xcfx89/|xcfx89xe2x88x92xcexa9i|]ni Ui.xe2x80x83xe2x80x83[19]
The dissipation on the ions is much greater than that on the electrons. The overall ion dissipation is minimized, however, if the frequency, xcfx89, is closer to the cyclotron frequency, xcexa9, of the minority low-mass ions. The power is proportional to the square of the density and xe2x88x92xc2xd power of the temperature. A density of 1018 mxe2x88x921 at a few eV temperature is reachable with a reasonable power.
One application of the present invention is isotope separation where the lighter isotope is minority and useful. Examples include lithium, boron, palladium and uranium. Furthermore, the methods of the present invention are more efficient than methods such as Dawson""s cyclotron resonance method in that the collector is not in the stream of the high-mass ions. Other applications for the separator include the separation of the fission products from the spent fuels (which consist mostly of TRU), and the separation of chemically similar elements.
In light of the above, it is an object of the present invention to provide devices and methods suitable for the purposes of efficiently separating a multi-constituent material into its individual constituents. It is another object of the present invention to provide methods for the separation of low-mass ions from high-mass ions in a multi-species plasma using ponderomotive forces. It is yet another object of the present invention to provide a device and method for the separation of low-mass ions from high-mass ions wherein the low-mass ion collector is not in the stream of the high-mass ions. Yet another object of the present invention is to provide a device and method for separating a material into its constituents which are easy to use, relatively simple to implement, and comparatively cost effective.
The present invention is directed to a device and method for separating a multi-constituent material into its individual constituents. To do this, the multi-constituent material is first converted into a multi-species plasma having ions of a relatively high-mass to charge ratio (Mh) and ions of a relatively low-mass to charge ratio (Ml). Specifically, this is done in a plasma chamber having two opposed ends which is provided to contain the multi-species plasma during separation. Further, the plasma chamber defines an axis extending through each end of the plasma chamber.
Coils are mounted on the outer surface of the plasma chamber to generate a substantially uniform magnetic field in the plasma chamber that is oriented parallel to the axis of the chamber. With this stationary magnetic field, moving ions with a relatively high-mass to charge ratio (Mh) will have a cyclotron frequency (xcexa9h) and moving ions with a relatively low-mass to charge ratio (Ml) will have a cyclotron frequency (xcexa9l).
The separation device of the present invention also includes an antenna for launching an electromagnetic wave into the plasma chamber that is evanescent in the multi-species plasma. Specifically, the antenna is positioned at one end of the plasma chamber to launch a wave into the plasma chamber through the chamber end. For the present invention, the electromagnetic wave is preferably elliptically polarized. As used here, the term xe2x80x9celliptically polarized electromagnetic wavexe2x80x9d includes circularly polarized electromagnetic waves. Importantly, the E vector of the elliptically polarized electromagnetic wave rotates at a frequency, a, and is rotated in the direction opposite to the orbit of the electrons in the stationary magnetic field (i.e. a left-hand polarized mode).
To obtain ion separation in accordance with the present invention, ponderomotive forces are generated that cause the low-mass ions to move in one direction while causing the high-mass ions and electrons to move in the opposite direction. In accordance with the mathematical equations presented above, this is achieved by using an electromagnetic wave having a frequency, xcfx89, where xcexa9h less than xcfx89 less than xcexa9I. Once the frequency, xcfx89, is established for the electromagnetic wave, a limit is placed on the density of light ions to ensure that the electromagnetic wave is evanescent in the multi-species plasma. For example, for a frequency, xcfx89=xc2xd[xcexa9h+xcexa9I], the density of light ions in the multi-species plasma is controlled to be less that ne/2, where ne is the density of electrons in the multi-species plasma. When collisional effects are anticipated (i.e. at high plasma densities), a frequency, xcfx89, for the electromagnetic wave is chosen to be closer in magnitude to xcexa9l than to xcexa9h to avoid power dissipation in the wave.